Teachers often wrongly presume that all students would interpret a three-dimensional image presented in a two-dimensional manner in the same way. They need to be specific as to how questions are stated especially in real-life situations, where alternative interpretations are possible.

A program on calculus is conducted, which helps students learn about inherent differentiation through a study of mathematical functions, while simultaneously reinforcing their understanding of functional concepts. This process develops their mathematical experience in the field of calculus and in other advanced quantitative programs.

The problem considered in this paper demonstrates that quite profound and inherently fascinating mathematics is accessible to students who have a sound number sense and deep conceptual understanding of very basic mathematics. This is one of many reasons why we should teach mathematics in ways that promote these attributes in students.

Tennis is a sport in which the mathematics involves an unusual scoring system together with other applications pertinent to the draw for different types of tournaments and the relative ratios of points won and lost. The name of the sport is thought to have originated from the French word "tenez", which translates roughly as "to receive (the…

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…

The usage of poetry for learning mathematics is discussed. Formula poetry involves repetition instead of rhyme and is thus useful in understanding mathematical concepts.

This paper analyses a lecture by an excellent teaching award winner professor of mathematics, given to high school mathematics teachers. The analysis is based upon two sources: (i) the lecture plan, as expressed in a series of 29 transparencies, prepared by the lecturer in advance; (ii) the actual implementation of the lecture, as transcribed from…

The starting point for this discussion of error estimates is the fact that integrals that arise in Fourier series have properties that can be used to get improved bounds. This idea is extended to more general situations.

Consider a sequence recursively formed as follows: Start with three real numbers, and then when k are known, let the (k +1)st be such that the mean of all k +1 equals the median of the first k. The authors conjecture that every such sequence eventually becomes stable. This article presents results related to their conjecture.

As the title says, this article considers the dog-on-the-beach problem from the perspective of the calculus of variations, making connections with the brachistochrone problem and Snell's law.

While waiting for his meal to arrive, a truck driver was using his straw to move water from one glass to another when he was struck by this question: If I keep doing this, will the two glasses ever have exactly the same amount of water? This article looks at various problems related to that question.

A quadrilateral is arithmetic if its area is an integer and its sides are integers in an arithmetic progression, and it is cyclic if it can be inscribed in a circle. The author shows that no quadrilateral is both arithmetic and cyclic.

When discussing the topic of elementary complex variables, students are often mystified by the fact that ii is real. After seeing a proof of this statement, a standard question is "well, what about iii or iiii etc., are these real or complex?" In this paper the meaning of the infinite power-tower iii...is considered both from the "bottom-up" and…

This paper considers rules for multiplying exponential and radical expressions of different bases and exponents and/or roots. This paper demonstrates the development of mathematical concepts through the application of connections to other mathematical ideas. The developed rules and most of the employed connections are within the realm of secondary…

Despite its intuitive appeal and popularity, Thorndike's constant ratio (CR) model for unbiased selection is inherently inconsistent in "n"-free selection. Satisfaction of the condition for unbiased selection, when formulated in terms of success/acceptance probabilities, usually precludes satisfaction by the converse probabilities of…